关于多项式Wolff公理
On the polynomial Wolff axioms
摘要：
我们证实了一个猜想的Guth关于最大数目的$δ$ -管，与$δ$ -分离的方向，包含在$δ$ -邻域的一个真正的代数簇。模因子$δ^{-\varepsilon}$，我们还证明了Guth和Zahl的广义版本的半代数集。虽然应用程序是在调和分析中找到的，证明将采用代数和微分几何，包括塔斯基的投影定理和格罗莫夫的代数引理深结果。
英文摘要：
We confirm a conjecture of Guth concerning the maximal number of $δ$-tubes, with $δ$-separated directions, contained in the $δ$-neighborhood of a real algebraic variety. Modulo a factor of $δ^{-\varepsilon}$, we also prove Guth and Zahl's generalized version for semialgebraic sets. Although the applications are to be found in harmonic analysis, the proof will employ deep results from algebraic and differential geometry, including Tarski's projection theorem and Gromov's algebraic lemma.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
